A physical template family for gravitational waves from precessing binaries of spinning compact objects: Application to single-spin binaries

The detection of the gravitational waves (GWs) emitted by precessing binaries of spinning compact objects is complicated by the large number of parameters (such as the magnitudes and initial directions of the spins, and the position and orientation of the binary with respect to the detector) that are required to model accurately the precession-induced modulations of the GW signal. In this paper we describe a fast matched-filtering search scheme for precessing binaries, and we adopt the physical template family proposed by Buonanno, Chen, and Vallisneri [Phys. Rev. D 67, 104025 (2003)] for ground-based interferometers. This family provides essentially exact waveforms, written directly in terms of the physical parameters, for binaries with a single significant spin, and for which the observed GW signal is emitted during the phase of adiabatic inspiral (for LIGO-I and VIRGO, this corresponds to a total mass M . 15M⊙). We show how the detection statistic can be maximized automatically over all the parameters (including the position and orientation of the binary with respect to the detector), except four (the two masses, the magnitude of the single spin, and the opening angle between the spin and the orbital angular momentum), so the template bank used in the search is only four-dimensional; this technique is relevant also to the searches for GW from extreme–mass-ratio inspirals and supermassive blackhole inspirals to be performed using the space-borne detector LISA. Using the LIGO-I design sensitivity, we compute the detection threshold (∼ 10) required for a false-alarm probability of 10 −3 /year, and the number of templates (∼ 76,000) required for a minimum match of 0.97, for the mass range (m1, m2) = [7,12]M⊙ × [1,3]M⊙.